Abstract
Simulation of the electrical and optical response of a multilayer thin film composed of lossless material coupled with adjacent lossy material in an alternating arrangement when applying a transverse voltage across the multilayer thin film is conducted using a polynomial approach. The modelling of the lossy–lossless multilayer thin film is a generalization of our previous work on multilayer thin film made up of alternating lossy–lossy materials. It is the propagation matrix of the electromagnetic wave in the thin film that governs its propagation, while the interface matrix represents the coupling between layers at an interface. The present solution models the multilayer thin film as an effective capacitor constructed from a series of coupled capacitors, with every layer being considered as a capacitor coupled to the next. A transverse voltage can affect the amounts of electric charges that accumulate at the interface between adjacent ‘capacitors’. The present model is constructed to describe nonmagnetic, lossy and lossless materials. With the aid of a home-developed code implementing the model, the reflection and transmission of multilayer Ge/MgO thin films are simulated. By tuning the transverse electric potential, geometrical and electrical parameters of an arbitrary lossy–lossless multilayer thin film, the code is capable of predicting nontrivial optical responses in terms of \(T\left(\lambda \right), R\left(\lambda \right), {\phi }_{T}\left(\lambda \right), {\phi }_{R}(\lambda )\). The code can serve as a useful tool for designing and optimizing lossless-lossy or lossless-lossless multilayer thin films to deliver desired optical functions.
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Data Availability
The refractive index of Germanium and Magnesium Oxide can be accessed by visiting and searching the database on the following website: acquired by K. company Filmetrics, “No Title refractive index data for common materials.” https://www.filmetrics.com/refractive-index-database. The electrical resistivity of Germanium can be found on the following website: https://periodictable.com/Elements/032/data.html. The dielectric constant of Germanium can be found on the following website: https://eesemi.com/sigegaas.htm. The electrical resistivity of Magnesium Oxide can be found in the reference (Yamaka and Sawamoto 1954). The dielectric constant of Magnesium Oxide can be found on the following website: https://www.crystran.co.uk/optical-materials/magnesium-oxide-mgo
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MM Halim and TLeong Yoon supervised the project and encouraged MKM Elhabbash to investigate " non-magnetic lossy multilayer thin films subjected to an external transverse voltage" and supervised the findings of this work. MKM Elhabbash conceived the presented idea, developed the theory, and performed the computations and simulations. TL Yoon and MKM Elhabbash verified the analytical methods. MKM Elhabbash wrote the manuscript with the support and supervision of TL Yoon and SA Taya. SA Taya checked the manuscript's plagiarism status, and MKM ElHabbash paraphrased it. All authors discussed the results and contributed to the final manuscript.
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Appendix flowchart and pseudocode of the wave tensor code
See Fig. 22.
Flow chart of the wave tensor code
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Elhabbash, M.K.M., Halim, M.M., Yoon, T.L. et al. A polynomial model of transmission and reflection of electromagnetic monochromatic plane waves in lossy, non-magnetic multilayer thin films subjected to an external transverse voltage. Opt Quant Electron 55, 214 (2023). https://doi.org/10.1007/s11082-022-04468-z
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DOI: https://doi.org/10.1007/s11082-022-04468-z